Differential Equations, Mathematical Modeling and Computational Algorithms: DEMMCA 2021, Belgorod, Russia, October 25–29

Preface
Contents
Some Classes of Quasilinear Equations with Gerasimov—Caputo Derivatives
	1 Introduction
	2 Non-degenerate Linear Equation
	3 Quasilinear Equation
	4 Degenerate Quasilinear Equation
	5 Examples
	References
On the Solvability of Initial Problems for Abstract Singular Equations Containing Fractional Derivatives
	1 Introduction
	2 Generalized Euler–Poisson–Darboux Differential Equation
	3 Generalized Functional-Differential Bessel–Struve Equation
	4 Appendix
	References
Local Bifurcations of Periodic Traveling Waves in the Generalized Weakly Dissipative Ginzburg-Landau Equation
	1 Introduction
	2 Formulation of the Problem
	3 Stability Analysis of Periodic Traveling Waves
	4 Turing—Prigogine Bifurcation
	5 Conclusions
	References
Towards Discrete Octonionic Analysis
	1 Introduction
	2 Preliminaries and Notations
		2.1 Continuous Octonionic Analysis
		2.2 Discretisation of Octonionic Analysis
	3 The Discrete Stokes' Formula in Octonions
	4 Summary
	References
Axiomatic Method for Constructing  a Generalized Solution of a Mixed Problem for a Telegraph Equation
	1 Introduction
	2 A Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Deviation
	3 Mixed Problem for an Inhomogeneous Wave Equation with Zero Initial Deviation
	4 A Mixed Problem for an Inhomogeneous Wave Equation with a Nonzero Initial Deviation
	5 Mixed Problem for the Telegraph Equation
	6 The Term-by-Term Integration Theorem
	References
Non-local Substitutions for Liouville Equations with Three and Four Independent Variables
	1 On the Group Properties of Bianchi Equations
	2 Three-Dimensional Analogue of the Liouville Equation
	3 Fourth-Order Analogue of the Liouville Equation
	References
Convergence Rates of a Finite Difference Method for the Fractional Subdiffusion Equations
	1 Introduction
	2 Discretization Methods
		2.1 Spatial Semidiscrete Schemes
		2.2 Fully Discrete Schemes
		2.3 Regularity of the Solutions
	3 Truncation Errors
	4 Global Error Analysis
	5 Numerical Results
	6 Conclusion
	References
Degenerate Quasilinear Equations with Dzhrbashyan—Nersesian Derivatives and Applications
	1 Introduction
	2 Quasilinear Nondegenerate Equation
	3 Quasilinear Degenerate Equation
	4 Fractional Models of Viscoelastic Fluid Dynamics
	References
On a K-Homogeneous Metric
	1 K-Homogeneous Metric
	2 Investigation of Isometric Transformations for the K-Homogeneous Kipriyanov Metric
	3 Characteristics of the K-Homogeneous Kipriyanov Metric in the Case of a Single Singular Variable
	4 Investigation of Geodesic Lines for a K-Homogeneous Kipriyanov Metric
	References
Biooscillators in Models of Genetic Networks
	1 Introduction
	2 General Models
	3 Four-Dimensional Systems
	4 Three-Dimensional Systems and Six-Dimensional Systems
	5 Notes and Comments
	References
Numerical Method for Problem of Scattering by a Small Thickness Dielectric Layer on a Perfectly Conductive Substrate
	1 Problem Statement
	2 Reduction of the Problem to Integral Equations
	3 Numerical Scheme
	4 Calculation Examples and Discussion
	References
Invariants of Dynamical Systems with Dissipation on Tangent Bundles of Low-Dimensional Manifolds
	1 Introduction
	2 Example: Plane Pendulum in a Jet Flow
	3 Example of More General System with One Degree  of Freedom
	4 Invariants of Systems of Geodesic Equations
	5 Invariants of Potential Systems
	6 Invariants of Systems with Alternating Dissipation
	7 Spatial Pendulum in the Flow of the Incoming Medium
	References
B-subharmonic Functions
	1 Introduction
	2 Definitions
	3 B-harmonic Functions
	4 Weighted Spherical Mean
	5 B-subharmonic Functions
	References
Some Multi–dimensional Modified  G- and H-Integral Transforms on  mathfrakLoverlineν, overliner-Spaces
	1 Introduction
	2 Preliminaries
	3 mathfrakLoverlineν,overliner-Theory And the Inversion Formulas for the Modified H1 σ,κ-Transform
	4 mathfrakLoverlineν,overliner-Theory and the Inversion Formulas of the Modified G1σ, κ- transform
	5 mathfrakLoverlineν,overliner-Theory and the Inversion Formulas of the Modified G1σ, κ;δ-Transform
	References
On Sufficient Conditions of the Faddeev–Marchenko Theorem
	References
Variational Approach to Construction of Piecewise-Constant Approximations of the Solution of Dynamic Reconstruction Problem
	1 Introduction
	2 Previously Obtained Results
		2.1 Dynamics
		2.2 Input Data
		2.3 Assumptions
		2.4 Dynamic Reconstruction Problem
		2.5 Algorithm
		2.6 The Main Result
	3 The New Results
		3.1 New DRP Statement
		3.2 Algorithm for Solving the New DRP
		3.3 The Main Result
	4 Example
	5 Conclusion
	References
Discrete Operators and Equations: Analysis and Comparison
	1 Introduction
	2 The Concept of the Research
		2.1 Local Discrete Operators
		2.2 Discrete and Continual
		2.3 Infinite and Finite
	3 Discrete Functional Spaces
	4 Approximate Solutions
		4.1 Infinite Discrete Solutions
		4.2 Finite Discrete Solutions
	References
Pseudo-Differential Equations in Spaces of Different Smoothness Exponents on Variables
	1 Introduction
	2 Elliptic Pseudo-differential Operators
		2.1 Sobolev–Slobodetskii Spaces of Different Smoothness
		2.2 Model Operators and Equations
	References
Thermodynamic Limit in Vector Lattice Models
	1 Introduction
	2 The Gibbs Random Fields
	3 The Hamiltonians Space Hν of Limit Gibbs Fields
	4 The Extensive Asymptotics of Free Energy
	5 Conclusion
	References
Family of Smooth Solutions of Hyperbolic Differential-Difference Equation
	1 Introduction
	2 Construction of Solutions of Equation (1)
	3 Existence of Smooth Solutions of the Equation (1)
	References